Using factor analysis or principal components analysis or measurement-error models for biological measurements in archaeology?

I am a Canadian archaeologist (BSc in Chemistry) researching the past human use of European Atlantic shellfish. After two decades of practice I am finally getting a MA in archaeology at Reading. I am seeing if the habitat or size of harvested mussels (Mytilus edulis) can be reconstructed from measurements of the umbo (the pointy end, and the only bit that survives well in archaeological deposits) using log-transformed measurements (or allometry; relationships between dimensions are more likely exponential than linear).
Of course multivariate regressions in most statistics packages (Minitab, SPSS, SAS) assume you are trying to predict one variable from all the others (a Model I regression), and use ordinary least squares to fit the regression line. For organismal dimensions this makes little sense, since all the dimensions are (at least in theory) free to change their mutual proportions during growth. So there is no predictor and predicted, mutual variation of all the dimensions is the response (a Model II regression), and the fitted regression line must give equal weight to all the dimensions: common methods are major-axis (perpendicular distances between the line and all the points are minimised, in a principal-component-analysis way) and reduced major axis or standard-major-axis (perpendicular distances between the standardised points and the line are fitted, and then unstandardised).

I see that you literally wrote the book on regression. Do you know if it is possible to carry out major-axis or reduced-major-axis fitting in multiple linear regressions in SPSS, SAS or Systat (I know that it can’t be done in Minitab)?

Do you know if there are applications in R that carry out this type of analysis?

My reply: I’m a sucker for any email that begins, “I am a Canadian archaeologist.” I think there are various models out there that could work here, including factor analysis and measurement-error models. I’m no expert on this particular set of models, but they get used in psychometrics when there are many variable measurements. Maybe some commenters could help?